Edward Swartz

Ph.D. (1999) University of Maryland at College Park

Combinatorics and discrete geometry

My research centers on the interplay between combinatorics, geometry/topology and algebra with a special emphasis on matroids and f-vectors of simplicial complexes. Matroids are combinatorial abstractions of linear independence. Their enumerative properties have applications in a variety of fields, including graph coloring and flows, linear coding, arrangements of hyperplanes, and problems in reliability theory. My interest in matroids originally started with the discovery of a close connection between matroids and quotients of spheres by elementary abelian p-groups. More recently, I have used face rings to establish analogues of the g-theorem for simplicial polytopes for a variety of simplicial complexes.

Matroids and quotients of spheres, Mathematische Zeitschrift 241 (2002), 247–269.

Topological representations of matroids, Journal of the Amer. Math. Soc. 16 (2003), 427–442.

g-elements of matroid complexes, J. Comb. Theory Ser. B 88 no. 2 (2003), 369–375.

Lower bounds for h-vectors of k – CM, independence and broken circuit complexes, SIAM Journal on Discrete Mathematics 18 no. 3 (2005), 647–661.